RT Journal Article
T1 Fibred links from closed braids
A1 Montesinos Amilibia, José María
A1 Morton, Hugh R.
AB It is proven that every fibred link in the 3-sphere S3 with k components can be obtained as the preimage of the braid axis for a d-sheeted simple branched cover over S3, branched along a suitable closed closed braid, with d=max{k,3}. More generally, it is shown that every open book decomposition of a closed oriented 3-manifold arises in a similar way. A major step in the proof involves showing that given a compact surface with boundary expressed as a d-fold simple branched covering of the 2-disk, d≥3, every homeomorphism of the surface fixing the boundary is isotopic to a lift of a homeomorphism of the disk. Finally, this perspective on fibred links is applied to interpret the conjecture, due to J. Harer, that all fibred links arise from the trivial knot by a sequence of so-called Hopf plumbings in terms of Markov moves on braids. This is a rather long, detailed, and readable paper that can be recommended as an introduction to many of the ideas discussed. The work actually dates from 1984.
PB Oxford University Press (OUP)
SN 0024-6115
YR 1991
FD 1991
LK https://hdl.handle.net/20.500.14352/58615
UL https://hdl.handle.net/20.500.14352/58615
DS Docta Complutense
RD 26 feb 2024